# Curl and Convective Derivative

Suppose u is a vector-valued function. Is it true that
(∇×u)( (u⋅∇)u ) = (u⋅∇)(∇×u)⋅u

?

Please note the lack of a dot product on the first two terms of the RHS and the parenthesis around the second term of the LHS. I'm trying to understand whether these differential operators are associative.

andrewkirk
$$\nabla=\frac{\partial}{\partial x}+ \frac{\partial}{\partial y}+ \frac{\partial}{\partial z}$$
$$\mathbf{a\cdot b}=\sum_{k=1}^3 a_kb_k$$